I search for intermediate results for the following:

If one has an homomorphism between two structures in the
language of first-order logic with equality, say
A and B, then (it is well-known that) for all positive
formulas F, it holds that A |= F implies B |= F  
(where positive formulae means, formulae built up from
‘or’, ‘and’, existential and universal quantifiers).

On the other side if there is an isomorphism between
A and B, then for any formulae F, A |= F iff B |= F.

In Gallier’s book "Logic for Computer Science", one
can find definitions and intermediate results, but
unfortunately incorrect  (pp. 182 (problem 5.3.15. (c)).

             M. Ayala
             ay…@informatik.uni-kl.de

I’m reading the book An Introduction to Mathematical Logic: To Truth
Through Proof by Peter B. Andrews. He says (p 52) that a first order
logic wff A is a substitution instance of a tautology iff there is a
propositional calculus tautology B such that A has the form

  p1 … p(n)
S             B.
  C1 … C(n)

What does this mean? Is p(i) a propositional variable and C(i) a
first order logic wff?

–

Henry Choy
c…@cs.usask.ca

What do we explore now, Spock?
How about the wild sorority girls of the planet Playtex?

I’m trying to understand the proof of Lemma 2112 in An Intro
to Mathematical Logic and Type Theory: To Truth Through Proof
by Peter B. Andrews (like what else is there to do on Sunday?).

2112 Lemma. Suppose H |- A and let U be a finite set of individual
variables not free in A or H. Then there is a proof of A from H
such that no member of U is generalized upon or occurs free in any
wff of the proof.

He says it’s sufficient to prove the lemma for the case where H
is finite, but he never uses the idea of a finite H in the proof
so is finiteness a big deal?

Am I right to think that generalizing on a variable x is to say
"for all x"?

–
Henry Choy
c…@cs.usask.ca

I’ll have two all beef patties, special sauce, lettuce, cheese,
pickles, onions, on a sesame seed bun, please.

Is there any NP-complet problem which is linear on average ? Perhaps
the satisfiability of propositionnal calculus (with Boyer Moore
algorithm) ?

Christophe

–

———————————————————-
Christophe Raffalli

L.F.C.S. (Laboratory for Fundation of Computer Science)
Department of Computer Science, King’s building university
Edinburgh EH9 3JZ
———————————————————-

sorry i miquoted Plato that isn’t from the phaedo I believe.
Christian S. Morley

I tried to send in a fallacy for the Logical Argument FAQ for alt.atheism.
Only thing is, I can’t phrase it very well, nor do I know any good name for it.

Anyway, the fallacy (at least I _hope_ a fallacy) is as follows:

"You are doing X.  Doing X causes lots of misery.  Therefore you are causing
lots of misery."
"You want to do X.  Doing X causes lots of misery.  Therefore, you want to cause
lots of misery."

The first is a valid argument, and the second is not.  I believe there might
even be some special word for how "want" acts in sentences like these.  Can
someone give me some idea how to explain this well enough that I can submit it?
—
"On the first day after Christmas my truelove served to me…  Leftover Turkey!
On the second day after Christmas my truelove served to me…  Turkey Casserole
    that she made from Leftover Turkey.
[days 3-4 deleted] …  Flaming Turkey Wings! …
   – Pizza Hut commercial (and M*tlu/A*gic bait)

Ken Arromdee (arrom…@jyusenkyou.cs.jhu.edu)

I’ve been out of this for a while… From Gerhard Brewka: Nonmonotonic
reasoning: Foundation of Commonsense, I see

        T u ASS(T) |- p
 where  ASS(T) := { not q | q is atomic and not T |- q}

how do I read it?

Thanks,
—
-roffe
rolf.lindg…@usit.uio.no

In article <C7Byq8….@grebyn.com>

- Hide quoted text — Show quoted text -

f…@grebyn.com (Fiona Webster) writes:
>In response to my query about Lakoff and Johnson’s _Metaphors_We_
>_Live_By_, Ken writes:
>>From my point of view there are two problems with it:
>>        1. The notion that the "conventional metaphors" of our
>>language affect/determine how we think about reality (whence the
>>title) is pretty much just warmed-over Whorfianism:  Benjamin Lee
>>Whorf (& Edward Sapir) argued in the first half of the century that
>>the structure of a community’s language significantly determines how
>>the community thinks.  No empirical evidence for this view was ever
>>brought to bear and in the actual field of linguistics is not a live
>>issue.  The problem with all forms of Whorfianism is that

>>        2. It completely overlooks the historical dimension…
>I’m going way out on a limb here, because I certainly don’t know
>this field very well, but I thought that at least some of what
>George Lakoff writes goes in the mind-affecting-metaphor direction–
>i.e., opposite to that of the well-known and often-decried Whorf-
>Sapir point of view, which is metaphor-affecting-mind.  The subtitle
>of Lakoff’s _Women,_Fire_,and_Dangerous_Things_ is "What Categories
>Reveal about the Mind."  *If* (I’m not sure he is) Lakoff were
>coming from this brain-first direction, then the historical dimension
>would assume less importance, of course–because presumably our
>brains haven’t changed all that much in the past umpteem thousand
>years.

>Does Lakoff muddy the waters as to whether he’s talking about
>mind –> metaphor, vs. metaphor –> mind?  Is that the problem?

Don’t worry, — Lakoff doesn’t know this field very well, either.  In
fact, I’ve yet to discover any scholarly field in which he could claim
deep knowledge.  Not that it stops him from repeatedly making pompous
pronouncements regarding the plural subjects of his ignorance.  I am
especially tickled by his egregious misinterpretation of what he dubs
"Putnam’s Theorem", — a nearly trivial proposition from the Appendix
of _Reason, Truth and History_, where Putnam, in effect, shows that
isomorphic structures are elementarily equivalent.  This factoid is so
trivial, that I’ve yet to find it mentioned even as exercise, in any
of the numerous model theory texts in my possession.  I rather doubt
that Putnam is particularly fond of having his name associated with
this bit of fluff, rather than, say, numerous fundamental results in
the hierarchy theory, or diophantine sets.  I know for a fact that his
own interpretation of the said result is the very opposite of
Lakoff’s.  Not that this, or any other discrepancy with reality, could
ever persuade anyone of the fallaciousness of his arguments, nor dull
the meretricious appeal of his anti-realist dogma in linguistics.  On
the alternatives to which, see the writings of Jerrold Katz.

N.B.  The term "category theory" has a well-defined extension that has
nothing in common with the alleged subject matter of Lacoff’s
elucubrations.

>                                                    –Fiona

cordially,
mikhail zel…@husc.harvard.edu
"Le cul des femmes est monotone comme l’esprit des hommes."

                       KURT GOEDEL SOCIETY

                      Yearbook Back Issues

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YEARBOOK 1988
————-

HAO WANG:   The Kurt Goedel Society (Kurt-Goedel-Gesellschaft).
  An introductory note

WILFRID HODGES:   The Present Aims of Model Theory

ROMAN MANKA:   Some Forms of the Axiom of Choice

ALEXANDER LEITSCH:   On Some Formal Problems in Resolution Theorem Proving

KARL SVOZIL:   The Mathematical Foundations of Physical Randomness
  and Indeterminism

MATTHIAS BAAZ, GERALD QUIRCHMAYR:   Juridische Schluesse und mehrwertige Logik

PAUL ERDOS:   Recollections on Kurt Goedel

NORBERT BRUNNER:   Mathematische Induktion, Kontinuumshypothese und
  Auswahlaxiom

MAURICE BOFFA:   ZFJ and the Consistency Problem for NF

ANDREAS BLASS:   Axioms of Choice for Finite Sets

WINFRIED JUST:   Equivalence under Decomposition. A Graph-theoretical Approach  

Reviews
Announcement

YEARBOOK 1989
————-

A Note on this Volume

First Kurt Goedel Colloquium. Program

HAO WANG:   Mind, Brain, Machine

EGON BOERGER:   A Logical Operational Semantics of Full PROLOG

GERNOT SALZER:   Deductive Generalization for Clause Logic

CHRISTIAN FERMUELLER:   Deciding Some Horn Clause Sets by Resolution

DAMJAN BOJADZIEW:   Reconstructing Diagonalization(s)

MARIA LUISA DALLA CHIARA:   Intensions, Probabilities, and Logical
  Indeterminism in the Semantics of Quantum Theory

MAURICE BOFFA:   A Set Theory with Approximations

JOSEF MATTES:   Classes and Internal Set Theory

MATTHIAS BAAZ:   Automatisches Beweisen fuer endlichwertige Logiken

YEARBOOK 1990
————-

JOACHIM HILGERT:   Group Theoretical Aspects of Goedel’s Cosmological Model

JOHN C. SIMMS:   Why the Continuum Hypothesis is False

THOMAS JECH:   The Infinite

ERWIN ENGELER:  Zur wissenschaftstheoretischen Bedeutung der
  kombinatorischen Algebra

ECKEHART KOEHLER:   Goedel and Carnap in Vienna

HELENA RASIOWA:   On Approximation Logics: A Survey

HAO WANG:   Aperiodicity and Constraints

ULRICH FELGNER:   Pseudo-endliche Gruppen

ROBERT F. TICHY:   Zur Analyse und Anwendung von Zufallszahlen

A. R. D. MATHIAS:   Logic and Terror

YEARBOOK 1991
————-

Second Kurt Goedel Colloquium. Program

JAAKKO HINTIKKA:  Goedel’s Functional Interpretation in a Wider Perspective

JAAKKO HINTIKKA:   A Historical Note on Scott’’s _Game-theoretical
  Interpretation of Logical Formulae_

DANA SCOTT:    A Game-theoretical Interpretation of Logical Formulae

EDGAR G. K. LOPEZ-ESCOBAR:   Zeno’s Paradoxes: Pre Goedelian Incompleteness

MICHIEL VAN LAMBALGEN:   On Bernays’’ Platonism and the Axiom of Choice

THOMAS OBERDAN:    Goedel, Carnap, and the Thesis that Mathematics is Empty

JAN WOLENSKI:   Goedel, Tarski and the Undefinability of Truth

DANIELE MUNDICI:   Logic and Algebra in Ulam’s Searching Game with Lies

YEARBOOK 1992
————-

HAO WANG:   Imagined Discussions with Goedel and with Wittgenstein

PETER LOEB:   Nonstandard Analysis and Measure Theory

JOSEF MATTES:   Axiomatic Approaches to Nonstandard Analysis

VLADIMIR RUDENKO:   A New Result on the Horn Implication Problem

NORBERT ROZSENICH:   The Projective Goedel Universe

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In article <1ran8nINN…@darkstar.UCSC.EDU> i…@cse.ucsc.edu (ian barland (worm canner)) writes:

>Hi, i’m looking for simple, short, (but convincing proofs that 0 = 1.

Let X be the statement: if X then 0 = 1.

In particular, X is the statement:
          "’implies 0 = 1 if preceded by its quotation’
            implies 0 = 1 if preceded by its quotation"

(1) Proof that X implies 0 = 1:
Assume X.  Then by definition, if X then 0 = 1.  Therefore 0 = 1.

(2) Proof of X:
Since we have just shown that X implies 0 = 1, we’ve just proven the statement
if X then 0 = 1, thus by definition, X.

(3) Proof of 0 = 1:
Taking (1) and (2) together, it follows that 0 = 1.